深夜亚洲福利久久

21.1 Reconsideration of the laws of electromagnetism: Maxwell's equations

 

A good explanation of the origin of the displacement current may be found in the video lecture on and, in particular, in the lecture video clip .

The introduction of Maxwell's equations in many textbooks starts from a treatment of the laws of electromagnetism in vacuum (that is, in the absence of magnetic or polarisable media). This is the form of the equations that would be applied to the study of microscopic systems. In these circumstances, of course, electromagnetic theory can be completely described by just two vector fields (E and H or, more commonly, E and B).

Following the usual approach in Understanding Physics, however, Chapter 21 begins from a macroscopic viewpoint. In this case, a complete description of electromagnetisn requires all four vector fields E, D, H and B. This approach has the advantage of being generally simpler, consistent with what had gone before in earlier chapters and highlights the symmetries inherent in Maxwell's equations. One can easily transfer to the microscopic viewpoint by replacing D by e0E and B by m0H (or H by B/m0, if preferred.)

An inspection of the integral form of the equations (20.4a-d in Understanding Physics) shows the high degree of symmetry between the magnetic and electric quantities (even more evident when the possibility of free magnetic monopoles is considered as in the equations immediately above). Clearly D and B play similar roles, as do E and H; this is the rationale for treating D and B as flux densities and E and H as field strengths.

There is, on the other hand, a different symmetry in the laws of electromagnetism which can be seen from the Lorentz force (Section 19.7). The force on a charge q moving with velocity v in an electromagnetic field is F = qE + q(vB). From this viewpoint, E and B play similar roles and consequently these quantities are often referred to as the 'electric field' and the 'magnetic field', respectively.

Understanding Physics

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Mansfield and O'Sullivan, Understanding Physics, 3rd ed., John Wiley & Sons, Chichester (2020),

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